NBT-MAT
Notes
,ADVANTAGE NBT
NOTES
Function or Non-Function .................................................................................................... 2
Nature of Roots .................................................................................................................... 2
Real Number System ............................................................................................................ 3
Domain & Range .................................................................................................................. 4
Reading Off The Graphs ....................................................................................................... 4
Parabola ............................................................................................................................... 5
Hyperbola ............................................................................................................................. 6
Exponential Function ........................................................................................................... 6
Logarithm Functions ............................................................................................................ 7
Inverse Function ................................................................................................................... 8
Transformations with Respect to Functions ........................................................................ 8
Sequences ............................................................................................................................ 9
Quadratic Pattern (2nd level difference) ............................................................................... 9
Exponents........................................................................................................................... 10
Surds .................................................................................................................................. 10
Logarithms ......................................................................................................................... 11
Pythagagorus Theorm ........................................................................................................ 12
Lengths of Sides of Triangles .............................................................................................. 12
Area .................................................................................................................................... 13
Polygons ............................................................................................................................. 14
Surface Area & Volume ...................................................................................................... 15
Trigonometry......................................................................................................................... 16
Trigonometric Equations .................................................................................................... 18
Trigonometric Rules ........................................................................................................... 21
Circle Geometry ................................................................................................................. 22
Quadrilaterals..................................................................................................................... 25
Coordinate Geometry / Analytical Geometry ....................................................................... 26
Data Handling ..................................................................................................................... 27
Ratio ................................................................................................................................... 28
Problem Solving ................................................................................................................. 29
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, ADVANTAGE NBT
FUNCTION OR NON-FUNCTION
GIVEN FUNCTION NON-FUNCTION
Vertical line test – cut
GRAPH
once and only once.
RULE <; >; ≤; ≥; ≠
' is to the power of an
even number
If the rule is ( = *
Set of ordered ( − *,,-./01234 are
numbered pairs never repeated.
MAPPING
Horizontal line test One to One Many to Many
TO Vertical line test Many to One One to Many
NATURE OF ROOTS
567 + 96 + : = ;
Nature of Roots 97 − <5:
Equal roots = > − 41* = 0
1( > + =( + * is a square trinomial i.e
1( > + =( + * = 1 ( − A >
Real and equal roots = > − 41* = 0
Real Roots = > − 41* ≥ 0
Real and unequal roots = > − 41* > 0
Roots are rational = > − 41* = B> (perfect square)
Roots are irrational = > − 41* = 1 0,0 − B>
Roots are non-real = > − 41* < 0
©Advantage NBT. A division of Advantage Learning Technologies (Pty) Ltd. www.advantagelearn.com 2
Notes
,ADVANTAGE NBT
NOTES
Function or Non-Function .................................................................................................... 2
Nature of Roots .................................................................................................................... 2
Real Number System ............................................................................................................ 3
Domain & Range .................................................................................................................. 4
Reading Off The Graphs ....................................................................................................... 4
Parabola ............................................................................................................................... 5
Hyperbola ............................................................................................................................. 6
Exponential Function ........................................................................................................... 6
Logarithm Functions ............................................................................................................ 7
Inverse Function ................................................................................................................... 8
Transformations with Respect to Functions ........................................................................ 8
Sequences ............................................................................................................................ 9
Quadratic Pattern (2nd level difference) ............................................................................... 9
Exponents........................................................................................................................... 10
Surds .................................................................................................................................. 10
Logarithms ......................................................................................................................... 11
Pythagagorus Theorm ........................................................................................................ 12
Lengths of Sides of Triangles .............................................................................................. 12
Area .................................................................................................................................... 13
Polygons ............................................................................................................................. 14
Surface Area & Volume ...................................................................................................... 15
Trigonometry......................................................................................................................... 16
Trigonometric Equations .................................................................................................... 18
Trigonometric Rules ........................................................................................................... 21
Circle Geometry ................................................................................................................. 22
Quadrilaterals..................................................................................................................... 25
Coordinate Geometry / Analytical Geometry ....................................................................... 26
Data Handling ..................................................................................................................... 27
Ratio ................................................................................................................................... 28
Problem Solving ................................................................................................................. 29
©Advantage NBT. A division of Advantage Learning Technologies (Pty) Ltd. www.advantagelearn.com 1
, ADVANTAGE NBT
FUNCTION OR NON-FUNCTION
GIVEN FUNCTION NON-FUNCTION
Vertical line test – cut
GRAPH
once and only once.
RULE <; >; ≤; ≥; ≠
' is to the power of an
even number
If the rule is ( = *
Set of ordered ( − *,,-./01234 are
numbered pairs never repeated.
MAPPING
Horizontal line test One to One Many to Many
TO Vertical line test Many to One One to Many
NATURE OF ROOTS
567 + 96 + : = ;
Nature of Roots 97 − <5:
Equal roots = > − 41* = 0
1( > + =( + * is a square trinomial i.e
1( > + =( + * = 1 ( − A >
Real and equal roots = > − 41* = 0
Real Roots = > − 41* ≥ 0
Real and unequal roots = > − 41* > 0
Roots are rational = > − 41* = B> (perfect square)
Roots are irrational = > − 41* = 1 0,0 − B>
Roots are non-real = > − 41* < 0
©Advantage NBT. A division of Advantage Learning Technologies (Pty) Ltd. www.advantagelearn.com 2
